DOI QR코드

DOI QR Code

Bilinear elastodynamical models of cracked concrete beams

  • Pandey, Umesh Kumar (Department of Civil Engineering, National Institute of Technology) ;
  • Benipal, Gurmail S. (Department of Civil Engineering, Indian Institute of Technology Delhi)
  • 투고 : 2010.02.16
  • 심사 : 2011.05.25
  • 발행 : 2011.08.25

초록

Concrete structures are generally cracked in flexural tension at working loads. Concrete beams with asymmetric section details and crack patterns exhibit different flexural rigidity depending upon the sense of the applied flexural moment. In this paper, three different models, having the same natural period, of such SDOF bilinear dynamical systems have been proposed. The Model-I and Model-II have constant damping coefficient, but the latter is characterized by two stiffness coefficients depending upon the sense of vibration amplitude. The Model-III, additionally, has two damping coefficients as well. In this paper, the dynamical response of Model-III to sinusoidal loading has been investigated and compared with that of Model-II studied earlier. It has been found that Model-III exhibits regular and irregular sub-harmonics, jump phenomena and strong sensitivity to initial conditions, forcing frequency, system period as well as the sense of peak sinusoidal force. The constant sustained load has been found to affect the natural period of the dynamical system. The predictions of Model-I have been compared with those of the approximate linear model adopted in present practice. The behaviour exhibited by different models of the SDOF cracked elastic concrete structures under working loads and the theoretical and practical implications of the approach followed have been critically evaluated.

키워드

참고문헌

  1. Agarwal, P. and Shrikhande, M. (2006), Earthquake Resistant Design of Structures, Prentice Hall of India Private Ltd., New Delhi.
  2. Bayissa, W.L. and Haritos, N. (2004), "Experimental investigation into vibration characteristics of a cracked Tbeam", Proceedings of the Conference of Australasian Earthquake Engineering Society, Mt. Gambier, South Australia.
  3. Benipal, G.S. (1994), "Rational mechanics of reinforced concrete beams", Proceeding National Symposium on Structural Mechanics, I.I. Sc. Bangalore, India, June.
  4. BIS-IS: 1893-2002: Indian Standard Code of Practice-criteria for Earthquake Resistant Design of Structures, Bureau of Indian Standards, New Delhi.
  5. BIS-IS: 456-2000: Indian Standard Code of Practice for Plain and Reinforced Concrete, Bureau of Indian Standards, New Delhi.
  6. Carrion, F.J., Lozano, A. and Castano, V.M. (2006), "Condition monitoring of vibrating steel-reinforced concrete beams through wavelet transforms", Struct. Surv., 24(2), 154-162. https://doi.org/10.1108/02630800610666682
  7. Chen, G., Yang, X., Ying, X. and Nanni, A. (2006), "Damage detection of concrete beams using nonlinear features of forced vibration", Struct. Hlth. Monit., 5(2), 125-141. https://doi.org/10.1177/1475921706057985
  8. Chopra, A.K. (1995), Dynamics of Structures, Prentice-Hall of India, New Delhi.
  9. Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, McGraw Hill, Singapore.
  10. Chung, Y.S., Park, Y.G., Cho, S.H. and Lee, K.M. (1999), "Experimental study on the dynamic characteristics of a vibration controlled concrete beam", Proceedings of the 15th International Conference on Structural Mechanics in Reactor Technology (SMIRT 15) Held at Seoul, Korea, August.
  11. de Haan, Y.M. and Sluimer, G.M. (2001), "Standard linear solid model for dynamic and time dependent behavior of building material Heron", Heron, 46(1), 49-76.
  12. Demaric, G.V. and Sabia, D. (2011), "Non-linear damping and frequency identification in a progressively damaged R.C. element", Exper. Mech., 51(2), 229-245. https://doi.org/10.1007/s11340-010-9360-4
  13. Eccles, B.J., Owen, J.S., Choo, B.S. and Woodings, M.A. (1999), "Nonlinear vibration of cracked reinforced concrete beams", Proceedings of the 4th Conference of European Association of Structural Dynamics (EURODYN), Prague, Czechoslovakia.
  14. Hossain, M.Z., Mizutani, K. and Sawai, H. (2002), "Chaos and multiple periods in an unsymmetrical spring and damping system with clearance", J. Sound Vib., 250(2), 229-245. https://doi.org/10.1006/jsvi.2001.3920
  15. Humar, J.L. (2002), Dynamics of Structures, A.A. Balkema Publishers, Tokyo.
  16. Huszar, Z. (2008), "Vibrations of cracked reinforced and prestressed concrete beams", Arch. Civil Eng., 6(2), 155-164. https://doi.org/10.2298/FUACE0802155H
  17. Musial, M., Kaminski, M. and Ubysz, A. (2009), "Free vibration frequencies of the cracked reinforced concrete beams-Methods of calculations", Proceedings of the 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, (Eds. K. Gurlebeck and C. Konke), Weimar, Germany, July.
  18. Natsiavas, S. (1990), "On the dynamics of oscillators with bilinear damping and stiffness", Int. J. Nonlin. Mech., 25(5), 535-554. https://doi.org/10.1016/0020-7462(90)90017-4
  19. Ndambi, J.M., Peeters, B., Maeck, J., De Visscher, J., Wahab, M.A., De Roeck, G. and De Wilde, W.P. (2000), "Comparison of techniques for modal analysis of concrete structures", Eng. Struct., 22(9), 1159-1166. https://doi.org/10.1016/S0141-0296(99)00054-1
  20. Neild, S.A., Williams, M.S. and McFadden, P.D. (2003), "Non-linear vibration characteristics of damaged concrete beams", J. Struct. Eng.-ASCE, 129(2), 260-268. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(260)
  21. Newtson, C.M., Gaur, P.J. and Brian, T.E. (2006), "Fundamental frequency testing of reinforced concrete beams", J. Perform. Constr. Fac., 20(2), 196-200. https://doi.org/10.1061/(ASCE)0887-3828(2006)20:2(196)
  22. Pandey, U.K. and Benipal, G.S. (2006), "Bilinear dynamics of SDOF concrete structures under sinusoidal loading", Adv. Struct. Eng., 9(3), 393-407. https://doi.org/10.1260/136943306777641869
  23. Pandey, U.K. (2008), "Nonlinear elastodynamics of cracked concrete beams", PhD Thesis submitted at Indian Institute of Technology Delhi, New Delhi.
  24. Pauley, T. and Priestley, M.J.N. (1982), Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, New York.
  25. Penelis, G.G. and Kappos, A.J. (1997), Earthquake Resistant Concrete Structures, E & FN SPON, London.
  26. Salzman, A., Fragomeni, S. and Loo, Y.C. (2003), "The damping analysis of experimental concrete beams under free-vibration", Adv. Struct. Eng., 6(1), 53-64. https://doi.org/10.1260/136943303321625739
  27. Teguh, M., Saleh, F., Duffield, C.F. and Hutchinson, G.L. (2006), "Strength deterioration of nonprismatic reinforced concrete beams", Proceeding of first International Conference on Computational Methods (ICCM04), held at Singapore, Springer, 1805-1815.
  28. Thompson, J.M.T., Bokaian, A.R. and Ghaffari, R. (1983), Sub-harmonic and chaotic motions of a bilinear oscillator", IMA J. Appl. Math., 31, 207-234. https://doi.org/10.1093/imamat/31.3.207
  29. Thompson, J.M.T., Bokaian, A.R. and Ghaffari, R. (1984), "Sub-harmonic and chaotic motions of compliant offshore structures and articulated mooring towers", ASME J. Energy Resour. Tech., 106, 191-198. https://doi.org/10.1115/1.3231037
  30. Thompson, J.M.T. and Elvey, J.S.N. (1984), "Elimination of sub-harmonic resonances of compliant marine structures", Int. J. Mech. Sci., 26, 419-425. https://doi.org/10.1016/0020-7403(84)90031-6
  31. Thompson, J.M.T. and Stewart, H.B. (1986), Nonlinear Dynamics and Chaos, John Wiley and Sons, New York.
  32. Wang, Z., Man, X.C., Finch, R.D. and Jansen, B.H. (1998), "The dynamic behavior and vibration monitoring of reinforced concrete beams", J. Test. Eval., ASTM, 26(5), 405-419. https://doi.org/10.1520/JTE12022J
  33. Zhu, X.Q. and Law, S.S. (2007), "Nonlinear characteristics of damaged reinforced concrete beam from Hilbert- Huang transform", J. Struct. Eng.-ASCE, 133(8), 1186-1191. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:8(1186)
  34. Zhu, X.Q., Law, S.S. and Hao, H. (2009), "Damage assessment of reinforced concrete beams including the load environment", Struct. Eng. Mech., 33(6), 765-779. https://doi.org/10.12989/sem.2009.33.6.765

피인용 문헌

  1. Analysis of nonlinear dynamic behavior of electrically actuated micro-beam with piezoelectric layers and squeeze-film damping effect vol.77, pp.4, 2014, https://doi.org/10.1007/s11071-014-1384-3
  2. Numerical crack modelling of tied concrete columns under compression vol.10, pp.6, 2012, https://doi.org/10.12989/cac.2012.10.6.575
  3. Elastic Stability of Concrete Beam-Columns vol.17, pp.01, 2017, https://doi.org/10.1142/S021945541750095X
  4. A simplified method to estimate the fundamental frequency of skew continuous multicell box-girder bridges vol.11, pp.4, 2014, https://doi.org/10.1590/S1679-78252014000400006
  5. Vibration and stability of axially loaded cracked beams vol.44, pp.3, 2012, https://doi.org/10.12989/sem.2012.44.3.305
  6. Response of SDOF bilinear elasto-dynamical models of cracked concrete beams for El Centro earthquake vol.6, pp.3, 2013, https://doi.org/10.1080/19373260.2013.801146
  7. Vibration analysis of cracked frame structures vol.45, pp.1, 2013, https://doi.org/10.12989/sem.2013.45.1.033